compression of breast cancer images by principal component analysis

the principle of dimensionality reduction with pca is the representation of the dataset ‘x’in terms of eigenvectors ei ∈ rn  of its covariance matrix. the eigenvectors oriented in the direction with the maximum variance of x in rn carry the most      relevant information of x. these eigenvectors are called principal components [8]. assume that n images in a set are originally represented in matrix form as ui∈ rr ×c,  i = 1,......,n, where r and c are, repetitively, the number of rows and columns of the matrix. in vectorized representation (matrix-to-vector alignment) each ui is a n = r × c- dimensional vector ai computed by sequentially concatenating all of the lines of the matrix ui. to compute the principal components the covariance matrix of u is formed and eigen values, with the corresponding eigenvectors, are evaluated. the eigen vectors forms a set of linearly independent vectors, i.e., the base {φ} n i=1 which consist of a new axis system [10]